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by Kenneth Kin Lum

You just did some probability calculations, and don't know if the answers are
correct.  So you write a program to verify the results.  If you have eight dice,
and throw them all at once, what is the probability that there are AT LEAST
three fives?  Try to write a program that find out the "number of desirable
outcomes" / "number of possible outcomes" by iterating through all the possible
outcomes of the dice throw.
 
It has a verbose mode to see that the program is running correctly (for the case
2 dice, at least 1 five):

	C:\rails\depot>ruby dice.rb -v 2 1
	         1   [1,1]
	         2   [2,1]
	         3   [3,1]
	         4   [4,1]
	         5   [5,1]  <==
	         6   [6,1]
	         7   [1,2] 
	         8   [2,2]
	         9   [3,2]
	        10   [4,2]
	        11   [5,2]  <==
	        12   [6,2]
	        13   [1,3]
	        14   [2,3]
	        15   [3,3]
	        16   [4,3]
	        17   [5,3]  <== 
	        18   [6,3]
	        19   [1,4]
	        20   [2,4]
	        21   [3,4]
	        22   [4,4]
	        23   [5,4]  <==
	        24   [6,4]
	        25   [1,5]  <==
	        26   [2,5]  <== 
	        27   [3,5]  <==
	        28   [4,5]  <==
	        29   [5,5]  <==
	        30   [6,5]  <==
	        31   [1,6]
	        32   [2,6]
	        33   [3,6]
	        34   [4,6]
	        35   [5,6]  <== 
	        36   [6,6]
	
	Number of desirable outcomes is 11
	Number of possible outcomes is 36
	
	Probability is 0.3055555555555556

	C:\rails\depot>ruby dice.rb 8 3
	
	Number of desirable outcomes is 226491
	Number of possible outcomes is 1679616
	
	Probability is 0.1348468935756745

It also has a "sample mode" to print out the samples every 50,000 times in the
loop:

	C:\rails\depot>ruby dice.rb -s 8 3
	         1   [1,1,1,1,1,1,1,1]
	     50001   [3,6,3,4,3,1,2,1]
	    100001   [5,5,6,1,6,1,3,1]
	    150001   [1,5,3,5,2,2,4,1]
	    200001   [3,4,6,2,5,2,5,1] 
	    250001   [5,3,3,6,1,3,6,1]
	    300001   [1,3,6,3,4,3,1,2]
	    350001   [3,2,3,1,1,4,2,2]
	    400001   [5,1,6,4,3,4,3,2]
	    450001   [1,1,3,2,6,4,4,2]
	    500001   [3,6,5,5,2,5,5,2]  <==
	    550001   [5,5,2,3,5,5,6,2]  <== 
	    600001   [1,5,5,6,1,6,1,3]
	    650001   [3,4,2,4,4,6,2,3]
	    700001   [5,3,5,1,1,1,4,3]
	    750001   [1,3,2,5,3,1,5,3]
	    800001   [3,2,5,2,6,1,6,3]
	    850001   [5,1,2,6,2,2,1,4]
	    900001   [1,1,5,3,5,2,2,4] 
	    950001   [3,6,1,1,2,3,3,4]
	   1000001   [5,5,4,4,4,3,4,4]
	   1050001   [1,5,1,2,1,4,5,4]
	   1100001   [3,4,4,5,3,4,6,4]
	   1150001   [5,3,1,3,6,4,1,5]
	   1200001   [1,3,4,6,2,5,2,5]
	   1250001   [3,2,1,4,5,5,3,5]  <== 
	   1300001   [5,1,4,1,2,6,4,5]
	   1350001   [1,1,1,5,4,6,5,5]  <==
	   1400001   [3,6,3,2,1,1,1,6]
	   1450001   [5,5,6,5,3,1,2,6]  <==
	   1500001   [1,5,3,3,6,1,3,6]
	   1550001   [3,4,6,6,2,2,4,6]
	   1600001   [5,3,3,4,5,2,5,6]  <==
	   1650001   [1,3,6,1,2,3,6,6]
	
	Number of desirable outcomes is 226491
	Number of possible outcomes is 1679616
	
	Probability is 0.1348468935756745